A Brief Introduction To Logic and Argumentation

7/29/2019 A Brief Introduction To Logic and Argumentation

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A Brief Introduction To Logic

and Argumentation What is an argument?

A series of claims,

known as premises,

that are arranged tocompel agreement

with a conclusion.

Two basic ways of criticizing an argument

(Keep these in mind):

1) Question the truth of the premises

2) Question that the conclusion follows from the premises


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Two basic kinds of arguments:

1) Deductive

a. Strongest kind, when done right they

guarantee their conclusion if premises are

true.

b. Quality is either/or, black and white, strong

or weak, no degrees.

c. Also really hard to do well.


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Two basic kinds of arguments:

2) Inductive

a. Weaker kind, when done right the best they

do is make their conclusion highly likely.

b. Quality is a matter of degree, never

absolutely air-tight (can be absolutely flawed.)

c. To an extent, quality is a matter of

interpretation. d. Thankfully, easier to do well.


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Deductive arguments and Validity:

When a deductive argument guarantees that the

conclusion follows from the premises it is called

valid; otherwise, it is invalid. Example of a valid argument:

1) If the moon is made of green cheese then God

exists.

2) The moon is made of green cheese.

3) Therefore, God exists.

The fact that premises (1) and (2) are false doesnt matter.

Validity is a matter of the FORM or STRUCTURE of anargument.


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Deductive arguments and Validity:

Notice the structure of the aboveargument:

1) If A then B.

2) A. 3) Therefore B.

This structure will ALWAYS be valid, (thatis, 3 will always follow from 1 and 2)regardless of what you plug in for A and B.


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Truth and Soundness

But what about truth? In a valid deductive argumenttrue premises will entail a true conclusion.

If a deductive argument has a valid structure AND all

of its premises are true, then it is a soundargument. A sound argument guarantees the truth of its

conclusion because (1) the premises are true and (2)its valid.

Soundness = valid structure + true premises.

Example of a sound argument: 1) All men are mortal

2) Socrates is a man 3 Therefore Socrates is mortal


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Truth without Validity

But just because an argument has truepremises/ conclusion doesnt mean its sound; itmay not have a valid structure. Consider: 1) If you are in Kingwood, then you are in Texas.

2) You are in Texas.

3) Therefore you are in Kingwood.

Even though all three are true (3) doesnt follow

from (1) and (2). The conclusion is not guaranteed by the

premises, so it is not valid and it is not sound.


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Invalid Structure

Note that the structure of the above argument

will ALWAYS be invalid

1) If A then B

2) B 3) Therefore A.

The If Then operator only gets you validity

when it goes forward (from the first term to the

second term), not when it goes backward.


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Inductive Arguments and

Inductive Strength: Four Types of Inductive Arguments:

1) Inductive Generalization

2) Argument from Analogy

3) Inference to the Best Explanation

4) Reductio ad Absurdum


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Inductive Generalization

In science this is basic hypothesis formulation

1) All/most of the observed Xs have been Y.

2) Therefore all/most of Xs are Y.

Two questions to ask:

(a) How representative is the sample?

(b) How reasonable is the conclusion, given

the evidence?


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Argument from analogy

1) X is like Y in certain relevant ways

2) Y has feature Z

3) Therefore X has feature Z

Two questions to ask: (a) are the relevant ways really relevant?

(b) are there any relevant dissimilarities?


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Inference to the best

explanation

1) X explains/accurately predicts A, B & C.

2) Y explains/accurately predicts A, B & C,

plus D, E & F. 3) There isnt anything that X

explains/accurately predicts that Y doesnt.

4) Y doesnt make more false predictions than

X. 5) Y is more simple and graceful than X.

(Occams razor)

6) Therefore Y (or rather, therefore Y over ofX.)


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Inference to the best

explanation Two questions to ask:

(a) Are there any other alternatives besides X

and Y?

(b) How, exactly, does Y explain/predict A, B,

C, D, E and F?


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Reductio ad absurdum

Can be deductive or inductive:

1) Assume P for the sake of argument

2) If P, then Q

3) But clearly ~Q (Q is absurd/false/unacceptable,etc.)

4) Therefore not P

Two questions to ask: (a) Does Q reallyfollow from P?

(b) Is Q really absurd, false, unacceptable, etc?


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A Few Common Fallacies:

Fallacies are common errors in reasoning.

Examples: Begging the question

Appeal to authority

Equivocation False analogy

False dilemma

Ad hominem

Straw Man Arguments from ignorance

Correlative fallacy (post hoc, ergo propter hoc)


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Begging the question:

Assuming the very thing youre trying to

prove, smuggling the conclusion into the

premises. Also called circular reasoning.

1) George says hes an honest man.

2) An honest man doesnt lie.

3) Therefore, I can trust George when he says

hes an honest man.


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Appeal to Authority

No substantive argument can ever be settled by

simplyinvoking an expert.

Experts can establish the truth of certain premises,but whether or not the conclusion follows is an open

question.

Frequently we dont have the time to investigate the

evidence for an argument ourselves, so we have no

choice but to (provisionally) accept the appeal to

authority.

1) Tom says global warming is real.


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Equivocation

Changing the meaning of a term in the

middle of an argument.

1) My money is in a bank.

2) A bank is the slope of land adjacent to a

river.

3) Therefore my money is in a slope of land

adjacent to a river.


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False Analogy

A failed argument from analogy; anargument that analogizes two things

which are not relevantlysimilar, butinstead are only superficially orapparently similar.

1) Women are like tornados: they tear your

life apart when they enter it and take yourstuff with them when they leave.

2) Tornados are meteorologicalphenomena.

3) Therefore, women are meteorological


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FalseDilemma

Presents only two alternatives for

consideration when other alternatives

exist.

Either youre with us or youre with the

terrorists.


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Ad hominem:

Attacking the person making the argument,rather than the argument itself. Sometimes this can be vicious (of course youd think

that, youre bleeding heart liberal!)

But other times it can be more subtle (Plato onlyrejected democracy because he grew up in HellenicGreece.)

Important to note: ad hominem CAN be a

legitimate response when were being asked tobelieve a CLAIM; its only inappropriate as arebuttal to an ARGUMENT.


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Straw Man:

Mischaracterizing an opponents position/argument so that it can be easily rebutted.

1) X thinks animals should have equal rights withhumans.

2) This entails that animals should have the right tovote. This is absurd.

3) Therefore X is wrong; animals shouldnt have

equal rights with humans.

The converse of this is theprinciple of charity:always make your opponents arguments as

strong as you can before trying to rebut them.


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Arguments from ignorance:

Assuming the lack of evidence FOR somethingconstitutes evidence AGAINST something.

I.E.-Even though there is no proof Aliens exist,

this doesnt count as proof that they DONTexist.

Note, sometimes this isnt a fallacy: Theres noproof Unicorns exist, but this DOES seem to

count as evidence that they DONT exist (if therewere any unicorns, we would have foundevidence.)

It depends if weve looked in the right places.


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Correlative fallacy:

Assuming a correlation is a cause. 1) The Supreme Court outlawed prayer in public

schools in 1962

2) The crime rate, divorce rate and teen pregnancy

rate have all drastically increased since 1962. 3) Therefore the lack of prayer in public schools has

been detrimental to society.

The conclusion MIGHT be true, but the

correlation alone does little to prove this or makeit plausible.


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Pirates cause Global Warming


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Its time to play Name That Fallacy!!!!

How many fallacies can

YOU spot in this clip?
http://www.youtube.com/watch?v=5KBqcOxIzTYhttp://www.youtube.com/watch?v=5KBqcOxIzTYhttp://www.youtube.com/watch?v=5KBqcOxIzTYhttp://www.youtube.com/watch?v=5KBqcOxIzTY

A Brief Introduction To Logic and Argumentation

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