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Elementary Logic

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Elementary Logic

PHIL 105-302

Intersession 2013

MTWHF 10:00 – 12:00

ASA0118C

Steven A. Miller

Day 2

“There’s beer in the fridge.”

When said to a visiting friend?

When said to a customer?

When speaking to an alcoholic partner?

Jon: We’re going out for drinks tonight.

Frank: If we’re doing that, let’s go to Sidetracks or The Cellar.

Jon: I’m banned from Sidetracks!

What’s the conclusion?

What’s implied?

The principle of charity: “in formulating implicit statements, give the arguer the benefit of the doubt; try to make the argument as strong as possible while remaining faithful to the arguer’s thought” (S, 12).

In general, try to be a friendly and helpful reader.

“If you were a real American, you wouldn’t oppose (the military / paying taxes / gun control / other issue of the day).”

Is it an argument?

What’s the implied conclusion?

The Cubs are the best C-named MLB team. We know this because the Cardinals are the worst MLB team, and the worst cannot be the best.

1) The Cubs are the best C-named MLB team.

2) The Cardinals are the worst MLB team.

3) The worst cannot be the best.

What’s the argument’s conclusion?

1) The Cubs are the best C-named MLB team.

2) The Cardinals are the worst MLB team.

3) The worst cannot be the best.

What’s missing / implied to complete it?

1) The Cubs are the best C-named MLB team.

2) The Cardinals are the worst MLB team.

3) The worst cannot be the best.

4) There are only two C-named MLB teams: the Cubs and the Cardinals.

In standard form:

1) There are only two C-named MLB teams: the Cubs and the Cardinals.

2) The Cardinals are the worst MLB team.

3) The worst cannot be the best.

4) [Therefore,] The Cubs are the best C-named MLB team.

Michelle Obama is the First Lady.

Michelle Obama has two daughters.

Michelle Obama has thirteen letters.

Michelle Obama has thirteen letters.

“Michelle Obama” has thirteen letters.

The first letter of Jingle Bells is “D.”

The first letter of “Jingle Bells” is “D.”

The first letter of the words to “Jingle Bells” is “D.”

These cookies cost twenty-five cents each. I have a dollar. I can buy four of them.

1.00 / x = y

x = .25

1.00 / .25 = y

4 = y

Informal logic:

If it’s dark, then it’s night.

It’s dark.

Therefore, it’s night.

Formal logic:

D ⊃ N

D

∴ N

D ⊃ N

D

∴ N

If I’m disappointed, then I’m nervous.

I’m disappointed.

And so I’m nervous.

Seventh Inning Stretch

(“Take Me Out to the Ballgame, …”)

What makes an argument good?

1) true premises

2) conclusion at least probable, given 1

3) premises are related to the conclusion

4) the conclusion can’t be undermined

1) true premises

In many cases, this is obvious:

“Carbondale is south of Chicago.”

“Carbondale is north of Chicago.”

But in others, it’s more problematic:

“There is a treasure chest buried 500 feet below where I stand.”

This truth of this latter kind is indeterminate.

1) true premises

For our purposes, we’ll treat the latter kind of sentence, the indeterminate ones, as true. Or, more properly, we’ll see what happens if they were to be true.

2) conclusion at least possible, given 1.

The concern here is that the argument is valid, which means that there is a particular kind of relationship between the premise(s) and conclusion.

Two kinds of argument:

deductive and inductive

1) deductive argument –

an argument in which the conclusion follows necessarily from the premises

deductive validity –

1) The conclusion necessarily follows from the premises.

2) If the premises are true, the conclusion must also be true.

3) It is impossible for the premises to be true and the conclusion to be false.

If it’s dark, then it’s night.

It’s dark.

Therefore, it’s night.

This argument is deductively valid:

If its premises are true, its conclusion cannot be false.

Bill drove to work.

Therefore, Bill must be over the age of 16.

Not necessarily valid: impossibility is not legal or practical but rather logical.

It is conceivable that Bill could be under 16 and driving to work, and so it is possible.

Bill drove to work.

Anyone who drives to work must be over the age of 16.

Therefore, Bill must be over the age of 16.

Valid.

A deductive argument is valid when

it is impossible (in the strongest sense)

for the premises to all be true

and the conclusion to be false.

2) inductive argument –

an argument in which the conclusion is likely to follow from the premises

91% of Polish people are Catholic.

Pitor is a Polish person.

We can conclude that Pitor is Catholic.

This argument is inductive:

If its premises are true, its conclusion may still be false.

1) Historians know of no civilizations that worshiped lizards.

2)So, humans never worshiped lizards.

Inductive.

1) No cats are purple.

2) Sashabear is a cat.

3) So, Sashabear is not purple.

Deductive.

1) The sidewalk is wet.

2) Usually, the sidewalk gets wet from rain.

3) It must have rained.

Inductive.

What makes an argument good?

1) true premises

2) conclusion at least probable, given 1

3) premises are related to the conclusion

4) the conclusion can’t be undermined